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I performed some measurements, which unfortunately include some noise. The measured signals are non-stationary, because the phenomena I am capturing is a transient.

Before the transient, I recorded a few seconds of background noise, so I have an idea of the noise that is also present during the transient.

How can I use this information to develop a proper de-noising technique?

I am thinking about using multi-resolution analysis (with the Discrete Wavelet Transform or the Empirical Mode Decomposition) to characterize and de-noise the signal.

However, I think that the information about the background noise could be of great help to develop this process. "Spectral subtraction" would apply only for stationary signals. Do you have any tips on how I can proceed in my case, in which the signal is non-stationary?

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